Study of Numerical Errors in DNS/LES
-
摘要: 通过比较湍流的能谱和总动能,对数值误差(包括混淆误差、离散截断误差)、亚格子模型以及它们之间相互作用对直接数值模拟和大涡模拟的影响进行了系统研究.算例采用了三维各向均匀同性湍流.为了研究复杂几何形状,数值格式采用了谱方法和Padé紧致格式.大涡模型采用了truncated Navior-Stokes(TNS)模型结合Padé离散滤波器.结果表明直接数值模拟中离散误差对结果有很大影响,低阶格式会导致计算发散.而大涡模拟中亚格子模型不仅能表征小尺度对大尺度的影响,而且还缓解了数值误差对计算结果的影响.因而低精度格式也可取得不错的结果.Abstract: By comparing the energy spectrum and total kinetic energy,the effects of numerical errors (which arise from aliasing and discretization errors),subgrid-scale(SGS) models and their interactions on direct numerical simulation(DNS) and large eddy simulation(LES) were investigated in detail.The decaying isotropic turbulence was chosen as the test case.In order to simulate complex geometries,both spectral method and Pad?compact difference schemes were studied.The truncated Navier-Stokes(TNS) equation model with Pad discrete filter was adopted as SGS model.It is shown that for DNS,discretization error plays a key role in the simulation.Low order difference scheme may be not suitable.While for LES,it is found that SGS model can not only represent the effect of small scales to large scales,but also dump the numerical errors.Thus low order discretization scheme can also obtain reasonable results.
-
Key words:
- numerical errors /
- TNS model /
- Pad compact difference scheme /
- discrete filter /
- LES
-
[1] Chow F K, Moin P. A further study of numerical errors in large-eddy simulations[J].Journal of Computational Physics,2003,184(2):366-380. doi: 10.1016/S0021-9991(02)00020-7 [2] Park N, Mahesh K.Analysis of numerical errors in large eddy simulation using statistical closure theory[J].Journal of Computational Physics,2007,222(1):194-216. doi: 10.1016/j.jcp.2006.07.016 [3] Davidson L.LESFOIL:an European project on large eddy simulations around a high-lift airfoil at high Reynolds number[A].In:European Congress on Computational Methods in Applied Sciences and Engineering[C].Barcelona,Spain,2000. [4] Mellen CP,Froehlich J, Rodi W. Lessons from LESFOIL project on large-eddy simulation of flow around an airforl[J].AIAA J,2003,41(4):573-581. doi: 10.2514/2.2005 [5] HE Guo-wei, WANG Meng, Lele S. On the computation of space-time correlations in decaying isotropic turbulence[J].Physics of Fluids,2004,14(11):3859-3867. [6] Ghosal S. An analysis of numerical errors in large-eddy simulations of turbulence[J].Journal of Computational Physics,1996,125(1):187-206. doi: 10.1006/jcph.1996.0088 [7] Kravchenko A, Moin P.On the effect of numerical errors in large eddy simulations of turbulent flows[J].Journal of Computational Physics,1997,131(2):310-322. doi: 10.1006/jcph.1996.5597 [8] Lund T. The use of explicit filters in large eddy simulation[J].Computers and Mathematics With Applications,2003,46(4):603-616. doi: 10.1016/S0898-1221(03)90019-8 [9] Vasilyev O, Lund T, Moin P. A general class of commutative filters for LES in complex geometries[J].Journal of Computational Physics,1998,146(1):82-104. doi: 10.1006/jcph.1998.6060 [10] Domaradzki J, Loh K, Yee P.Large eddy simulation using the subgrid-scale estimation model and truncated Navier-Stokes dynamics[J].Theor Comput Fluid Dyn,2002,15(6):421-450. doi: 10.1007/s00162-002-0056-y [11] Yang X, Domaradzki J.Large eddy simulations of decaying rotating turbulence[J].Physics of Fluids,2004,16(11):4088-4104. doi: 10.1063/1.1790452 [12] Lesieur M.Turbulence in Fluids[M].2nd Ed.Netherlands:Kluwer Academic Publishers, 1990. [13] Rogallo R. Numerical experiments in homogeneous turbulence[R]. NASA Tech Memo, 81835, 1981. [14] Lele S. Compact finite difference schemes with spectral-like resolution[J].Journal of Computational Physics,1992,103(1):16-42. doi: 10.1016/0021-9991(92)90324-R [15] Visbal M, Gaitonde D. On the use of higher-order finite-difference schemes on curvilinear and deforming meshes[J].Journal of Computational Physics,2002,181(1):155-185. doi: 10.1006/jcph.2002.7117 [16] YANG Xiao-long, FU Song. The effect of filtering on truncated Navier-Stokes equations[J].Journal of Turbulence,2007,8(8):1-18. doi: 10.1080/14685240600806256
点击查看大图
计量
- 文章访问数: 2758
- HTML全文浏览量: 83
- PDF下载量: 699
- 被引次数: 0